Phase-compensating network



39 5 .SR Wuwm July 15, 1930. H. NYQUIST 1,770,422

PHASE COMPENSATING NETWORK Fil ed Feb. 25, 1926 6 Sheets-Sheet INVENTOR -E,7Vygmst ATTORNEY Em x Em w Q NE 5 M Q 9 NF 3 M m m h ws I I l l hu a V I l m Q 3 y 15, H. NYQUIST 1,770,422

FHA SE COMPENSATING NETWORK Filed Feb. 25, 1926 6 Sheets-Sheet 3 Periods 7% ag k flllthase zlv edema; should 2 uab fthe corr g mndmq value A TTORNE Y INVENTOR I July 15," 1930.

H. NYQUIS T PHASE COMPENSATI-NG NETWORK Filed Feb. 25, 1926 30pm 0/ ('loseal I fire m: I I 01497115 6 Sheets-Shet 4 input |||0||| ltllOlC lnyout l v INVENTOR ATTORNEY ammo July 15, 1930.

H. NYQUIST PHASE COMPENSAT I NG NETWORK Filed Feb. 25, 1926 6 Sheets-Sheet 5 IN VEN TOR A TTORNEY July 15, 1930. H. NYQUIST 1,770,422

PHASE COMPENSATING NETWORK Filed Feb. 25, 1926 e Sheets-Sheet e INVENTOR Eijqzals A TTORNE Y Patented July 15, 1930 uniTEo STATES PA-TENT. OFFICE may NYQUIST, or firnLruRn, NEW JERSEY, assrenon 'ro AMERICAN TELEPHONE nm TELEGRAPH COMPANY, a coRronA'rIoN on NEW YORK PHA SE-COEPE NSATIN G NETWORK placement in time of the respectivefrequency components of a composite alternating current. Another object is to provide for a suitable phase shift of'currents of differentfrequencies in a circuit so asto bring them into a desired phase relation. Another object is to provide for a relative phase shift of the frequencycomponents in a transmission line to compensate for a normal phase shift in the line and to restore the components at the re- 1 special orms may ceiving end of the line to the same phase relation as though no line phase shift were present. Another object is to provide a transducer to operate .in tandem with a transmission line that shall compensate the distortion due to differential phaseshift on the line. Still another object is to provide a transducer to compensate for distortion due to a greater phase shift at high and low frequencies than at an intermediate frequency. In'the following specification with 'the accompanying drawings I disclose specific examples of practice according to my invention. It will .be understood that the specification relates largely to these particular cases and that the in-.

v'entionis defined in the appendedclaims. N

By the word transducer as employed in this specification, I mean any apparatus having a pair of input terminals for applied electromotive force and a pair of output terminals by which electromotive force may be applied to another element, the output being a function of the input. c Referring to the drawings, Figure. 1 is a .s mbolic diagram of afour-wire transmis- S1011 system embodying my invention; Fig. 2 is a dia ram .of a neral network of which emplov ed in embodying my invention; Fig. 3 is a diagram of a par- I Application filed February 25, 1926. Serial No. 90,656.

.ticular network used in an .embodiment of my invention here disclosed by 'way' of'illus- 4 tration; Fig. 4 is a diagram of delay-frequency characteristics to which reference will be made in explaining the principle of my invention, and the procedure for embodying it in a particular case; Fig. 5 is a diagram showing the relation of my improved dela network to other elements'of the system; ig. 6 is .a diagram showing delayas a function of frequency for certain transducers; Fig. 7

gives a family of delay-frequency characteristics that may affordguidance in the design of asuitable network in a particular case; Figs. 8, 9 and 10 show network sections equiv alent to type A of F ig.-. 3;. Fig. 11 shows a network section equivalent to type C of Fi' 3; Fig, 12 shows a plurality of sections, eaci like Fig. 11, connected in tandem; .Fig. 13 shows an equivalent for the combination of the two right-hand network sections of Fig. 12; Fig.14 shows anetwork section like Fig. 11 but with impedance elements made structurally complex to secure flexibility of design; Fig. 15 shows a network somewhat like Fig. 14 but arranged as a delay excursion ci'rcuit; Figs. 16 and 17 show simplified special case equivalents .for Fig. 15; Fig. 18 shows a delay excursion circuit arrangement by which the currents are made twice to traverse two sections of network like the two sections at the left in Fig. 12; Figs. 19, 20 'and 21 show sim lified special case equivalents for Fig. 18;

3; Figs. '27 and 27 show bridged-T sections equivalent to type B of Fig. 3; Figs. 27 and 27 show bridged-T sections equivalent to t pe C of Fig.3; Figs. 28 to 31, inclusive, s ow successive stages in the derivation of a network equivalent to Fig. 20 orFig. 21; Figs. 32 to 34, inclusive, are diagrams illustrating an alternative procedure for obtaining an equivalent delayexcursion circuit; and Fig. 35 is a curve diagram to be considered in connection with Fig. 34.

' The stations W and E of Fig, 1 are connected in a four-wire system by the two loaded lines Land L'tin eachof whichoccasional repeaters R are interposed. On the igs. 22 to 26,- inclusive, show bridged-T network sections equivalent to type C of Fig.

input side of each repeater B there are interposed a network P and an attenuation equalizer E intended to correct for distortion due to differential phase shift and attenuation on the line. Voice frequency currents put on the line L at station W go to the first repeater station, and then they pass through the phase distortion equalizer P which compensates for,

the differential, retardation of the components of the various frequencies by further retarding them unequally so that theyare brought to the same time relation to each other as at the sending end. Then the currents pass through the attenuation equalizer E and then through the amplifier R, and so on at each repeater station.

I will first assign specific values for the constants of a certain line and will give the specific design for the network of my invention in this instance, and thereafter I will discuss the principles on which this design is based and point out certain other examples of practice of the invention.

The line chosen for this first example is taken as a one-way No. 19 gauge medium heavy loaded cable circuit, 154 miles long, with a repeater at the middle and at the receiving end, and with a phase compensating network at the receiving end. The constants of the loaded line are:

Resistance R =95.5 ohms per mile at 1000 cycles per second;

Inductance L =0.154 henry per mile; Capacity C =0.065 microfarad per mile; Interval between loads= 1.136 miles. Assume that a wave train of a certain pure frequency f(=w/21r) is applied suddenly at one end of this line. As is well known, the received current at the other end will build up somewhat gradually. Let the time from the instant the sending current is applied until the received current reaches one-half its full steady-state value be represented b the letter T. This time T as a function 0 frequency f is shown by the curve marked Loaded line in Fig. 4. It will be seen that the delay is greater for the higher frequencies of the essential voice range.

The appropriate phase equalizing network of Fig. 3 consists of sections of three different types, eight sections of type A, six sections of type B and one section of type C. All these sections are special cases of the general crossed or lattice network of Fig. 2. The respective inductances and capacities in the network of Fi 3 have the values given in the following ta le:

L =0.5 henry;

C =0.2 microfarad;

L =0.25 henry;

C =0.1 microfarad;

L =O.42 henry;

L =0.059 henry;

C =0.024 microfarad;

C =0.17 microfarad.

The eight sections of type A by themselves have a delay-frequency characteristic as shown by the curve marked Type A in Fig. 4. When they are in tandem with the line, the resultant characteristic is shown by the dotted curve marked Line and type A.

It will be seen that the characteristic for the loaded line alone slopes up to the right and is concave up, and the characteristic for the type A network slopes down to the right and is concave up, and the resultant characteristic shown in dotted lines has an inter1nediate minimum. The additional sections of type B and type C are designed so that, by

transducer X over a certain frequency range will have a certain form, for example, as shown by the curve 12 in Fig. 6. Suppose it is desired that the currents shall go to receiver Z with their components of different frequency in the same time relation as at the generator G, in other words, so that all the components will be delayed equally and at the receiver the delay-frequency curve will be a horizontal line'such as g. This effect will be obtained by interposing a compensator whose characteristic 1' is complementary to p as shown in Fig. 6.

If the characteristic of the transducer X slopes up to the right as at p in Fig. 6, then the compensator Y should have a characteristic sloping down to the right as at 1". Sections of crossed type network, such as those of type A in Fig. 3, answer to this requirement, as will be seen by comparing curve r in Fig. 6 with the curve for type A in Fig. 4..

For a series of network sections like the one shown generallyin Fig; 2, and with the impedance values indicated thereon, the propagation constant I and the characteristic impedance K are given by the following formulas: I

It is desirable'that the characteristic impedance shall be areal constant K, and approximately the same as the impedance (resistance) of the elements with which the network is connected on the input and output sides. Assuming that the impedances 2 and 2 are diss ipationless, that is made up only of making L1 and the dependent value where-K is a real-constant and where's is a ure .reactance. -A network of the (type of i 2 with K constantis called a constant K network. Substituting in 1, it follows that H V A familiar formula of hyperbolic trigonometry is h 1 cosh I 1 tanh I'm-# 0 F (5) Substituting from (4), this reduces to I tanh I/2=z/2. (6)

Ingeneral, the propagation constant I may be put equal to a+ip, where a is the attenuationlconstant and B is the phase shlft constant. The structure for z is of react'a'nce elements only and on this basis it follows from Equation. (6-) that a=0, and that i tan B/2=z/2. (7)

gives B= 2 tan"w /L O (8) where w =2rrf, f being the frequency.

. It is approximately true that Hence b differentiating (8), the result is ob .tainedt at T- 2VL10" (10 By the aid of this equation, delay frequency characteristics'e'an be drawn for respective values of the product L G and from them it can readil be determined what is the best value of L 1 and how'many network sections are necessary get such compensation as should be effective for the type A sections. In this way, the number of sections for type A in Fi 3 has been fixed at eight, and the value of G at 10". The value of of C have been determined so that cuit so that For the sections oftype B or C, let the impedance 2 be made up of a seriesresonant cir.-

' where b. and 10,, are parameters to which we For the sections of type A of Fig. 3, this (6) and (11) it follows that tanh I/2=tanh 91,8/2= v j s rwo/ l the resonance frequency. For the type B network, V q

I b=2and4 Lg/O',.= K, g and the truth of Equation (11) will become apparent on noticing that I 'w ll'VLzOg,

and substituting for I2 andC in terms. of b and w in the equation truth of Equation (11) will become apparent in this case by substituting for L and C 1n terms of b and 40 in the equation Maw-L 0 As before, with I=a+z'B,

whence ffi= -*1 /erwo/ 3) V Difierentiating (l3) andsubstituting in (9),"'

in Fig. 7, which also shows that by 'ving to 1) increasing values, T can be ma em in crease at its maximum with accompanying decrease of values away from its maximum,

the area of the curve remaining constant. By increasing the number of sections of the network, Tcan be increased over the whole range for 10. Furthermore, 10,, may be chosen to put the maximum point at the right or left asmay be desired.

compensation efiected by type'A, this gives a minimum at or near 1000' c cles, or 105 =-2:1000. In Fig. 7 a series 0 curves is constructed with coordinates f/f and Tf., in-

stead of coordinates f and T as in Fig. 4. This is somewhat 'moreconvenient, and the curves from Equations Referring to Fig. 4, itis seen that after the I may assign proper values, tw /21 being of Fig. 7 can be utilized for any value of w...

Fi 4. fieferring again to the fact that each sec- Plotted either way, the area of each curve for a single section is unity. Hence we can estimate from the diagrams what value of b will be best and how many sections will he needful. In this way, the value b=2 is chosen and six sections of type B are found to be appropriate." Having chosen respective values for K, 'w and b, it follows from (3) and (11) that z /2=z'K/2=iwbK/2-w b'w K/iQ'w; and using the lettering of Fig. 3,

In type C, series L =bK/2'w' series C =2/b'w K.

In type B, since b=2,

series L =K/w series C l/w K. Also,

2 Z iw b bw 2K'w z'2wK and in type C, shunt (],=b/2K'w shunt L,=2K/bw In type B, since 1) =2,

shunt C =1/K'w shunt L =K/'w Fig. 4. t has already been mentioned that each section of type B or type C contributes about a unit area to the curves of Fig. 4 or 7 Each type A section contributes only about half a unit, but this is not necessarily to be looked on as a disadvantage, for the type A sections have only half as many reactance elements as the others.

The general procedure is first to plot the delay-frequency characteristic of the transducer to be compensatedas in the case of the curve marked Loaded line in Fig. 4. Then add sections like type A in proper number and with properly chosen reactance values so as to bring the ends of the characteristic up somewhere nearly to the same level. Then add sections like type B or C to raise the minimum dips in the curve up to nearly the level of the ends, and make the curve have nearly the same altitude all across the essential frequency range as for the uppermost curve of tion oftype B or type C contributes about a unit of area to the resultant curve of Fig. 4 or Fig. 7 (and half a unit for each section. of t pe A) it will readily be seen that this affor s a guide as to the number of sections that may need to be employed. Having given the Loaded line curve of Fig. 4, an ideal characteristic can be drawn higher up and the area between the two characteristics will give the number of sections of network that must be employed. The shorter the frequency range 15 made, the less the number of sections that will be required, but shortening the frequency range ma impair the quality in one way while the a dition of phase correcting network sections improves it in another way.

Assuming that economy of apparatus, particularly network sections, is a desideratum,

then it may be said that without unduly shortening the frequency range a resultant characteristic can be obtained which may be allowed to depart a little from the horizontal, and will require no more network sections than would be required to get a fully horizontal characteristic for a less frequency range. In other words, startin with a characteristic like that marked Loa ed line the optimum characteristic with proper economy of network sections will be a characteristic which extends over the whole desired frequency range but which slopes up alittle at the right and thus requires a less number of network sections than would be necessary to attain a completely horizontal characteristic over the same frequency range.

In the derivation of equivalents for network sections like those shown in Fig. 3, it will be convenient to represent type A of Flg. 3 as in Fig. 8. Fig. 9 is derived from Fig. 8 by the use of perfect transformers. The addition of these transformers has the advantage of permitting single reactance elements to be used where pairs of'reactance elements were required as in Fig. 8.

Another transformer arrangement that accomp)lishes the same result in reducing the num er of separate reactance elements 1s shown in Fig. 10, where a so-called hybrid coil or three-winding transformer is employed. Here, as in Fig. 9, the equivalence with Fig. 8 will be exact only when perfect transformers are employed.

Whereas Fig. 10 corres onds to t pe A of Fig. 3, Fig. ll correspon s to type of Fig. 3. Another distinction between Fig. '11 and Fig. 10 is that the number of distinguishable component coils in the hybrid coil has been reduced from five to three.

In Fig. 12 three network sections like Fig. 11 have been connectedin tandem in a manner apparent from the drawing. Between the middle section and the right-hand section, it will be seen that there are two transformers connected together without any intermediate apparatus. first step in the simplification of these two sections is to make them like 13 where the intermediate transformer win ings are omitted and the two transformers are consolidated into one transformer. v The reactance elements of a single network section can be made composite in such a way as to make the single section equivalent to a plurality of simpler sections in tandem. This principle can be employed to reduce the num-' ber of transformers in such an arrangement as that of Fig. 12 where the lurality of transformers may be objectiona le in that they add somewhat to the cost and introduce some electrical effects due to departure from the condition for perfect transformers. Thus in Fig. 14 a single section involving only one transformer is shown with its reactance ele- I to Fig. 16, but if the. connection at 53 is open,. Big? 27 R t 1 t f 1g. 1s an'a erna 1ve equ va en or chosen so that there is no reflection there.

While the direct wave produces a null'efi'ect in the secondary of the transformer 54, the unbalanced reflected wave is effective and gives a delayed output in the circuit of said secondary. By a suitable design of the network, the delay in the output canbe made to have difierent desired values for the different frequencies so as to compensate for delay in a connected transducer. I I

Reflection will occur at 53 whether the circuit there is closed or open, the only difl'erence being a difl'erence of Iphase. If the connection at 53 is closed, it ecomes equivalent it becomes equivalent to Fig. 17.

Another arrangement of an excursion circuit with a hybrid coil is shown in Fig'. 18 where the balancing resistance BB is on one side and on the other side is a pair of network sections like the middle and left section of Fig. 12 except that the com n'ent impedance elements are. shown symbo ically in- Fig. '18. ,Assuming that the circuit is closed at 53, Fig. 18 simplifies 'to Fig. 19, then to Fig. 20. v

' On the other hand, if'the circuit of Fig. 18 is to be left openat 53, then Fig. 18 re-. duces to Fig. 21. It will be apgrarent that in all these cases represented by i 15 to 21 it is possible to retain the simp e resistance BR as a balancing network; and in the resultant Figs. 20 and 21 the networks shown between the input terminals at the left and the output terminals at the right are all equivalentto four sections of lattice type network like any of the types of Fig. 3."

Z The bridged: network section of Fig. 22 is equivalent to the lattice C network section of Fig. 3. The equiva once is depend the reactance elements the w tween the members. One of these coils has a ne ative inductance which, of course, has no p ysical counterpart. But provided that L is greater than 4 23. can readily be realized physically in the network of Fig. 24;

Fi .25 is derived from Fig. 24 by the wellown substitution of a delta-for the star connection.

Another equivalent for Fig. 24 is obtained in Fig. 26 by substituting for the star a transformer of proper inductance values to be. the e uivalent of the star If is made equal to L then each of the four Figs. 23, 24, 25 and 26 reduces to Fig. 27 which is an equivalent brid ed-T network for the lattice type B networ of Fig. 3.

, the network of Fig.

The bridged-T network of Fig. 22 has the advantage over type C of Fig. 3 in that the total number of coils has been reduced from 4 to 2 and the total number of condensers has been reduced from 4 to 2. Another advantage of Fig. 22 over some equivalent net works that have been discussed is that no hybrid coil is involved. In Fi 26, only a single coil is used, subject to t 'e condition that it has an inductance coupling less than 'unity, and thus it embodies two magnetic circuits and is theoreticall the equivalent of two coils. Fig. 27 has t e practical advane tage that the two coils are equal and separate,'which simplifies construction and de- Fig. 27 and Figs. 27" and 27 are further equivalents for t pe C of Fig. 3.

Referring to igs. 20 and 21, it may be advantageous to consolidate the impedance elements represented by the symbols in the four boxes in each Thus the upper part of Fig. 20 first becomes like Fig. 28 where sists of three parts, one bridged across the entire transformer winding, and two bridged each across one-half of t 0 en to represent It is v well known that the latter two parts are equivalent to impedances of'four times the values of said parts bridged across the whole of the winding. This consideration leads to Fig. 30 as a further equivalent for Fig. 28, and in Fig. 31 the three impedances shown in multiple in Fig. 30 are consolidated to a sin le impedance. If the resulting network of Fig. 31 can be realized physically, it is substi'tuted back in Fig. 20 or 21, as the case ceedin tion with Figs. 32 to 35.

network. a

Fig. 34 shows a number of lattice type sections connected in tandem. These sections may be dissimilar, the only requirement being that they have a common impedance K. A resistance equal to K is connected to one end and the other end is either short circuited or left open. At this end there is complete reflection, whereas at the end where the resistance is located, there is no reflection at all,

the whole of the returning wave being absorbed in the resistance.

Now let a sinusoidal voltage E be applied at the input of Fig. 34. The value of the current into the network is E/2K. Let the phase change suffered by this current in traversing the network once be B/2. Then the* total phase change for the reflected wave having traversed the network in both directions is B when the far end is short-circuited, and differs from B by 1r radians when the'far-end is open-circuited. Hence in the two respective cases the current is:

Accordingliy the total current flowing into the resistance rom the network is equal to (I icos Bz' sin B).

or I A (1'-cos B-HI sin B) according as the switch at the right of Fig. 34 is closed or open. It follows that the total steady-state impedance is respectively 2K- 1+cos 6-11 sin 6 Hence the impedanceof the network is obtained by subtracting K fromeither of the foregoing expressions giving a result which simplifies respectively to Fig, 35 gives a plot of Z /z' K =tan B/2 for the first of these alternative expressions, that is,

tive values. There is a discontinuity at the point where Z reaches infinity, and for great er values of frequency, it reappears as a large negative value. With this definite guide to what is required, the network Z of Fig. 33 can be determined approximately and made to replace the series of lattice sections of Fig. 32.

What isazlaimed is:

1. In combination, a transducer giving different delays for different frequencies over a certain frequency range and a delay compensator giving compensatory delays for the respective frequencies, said delay compensator being connected in tandem with the said transducer and comprising a plurality of sections with one or more transformers incorporated in them, atleast one such transformer having at least three circuits connected therewith and a reactance element in one such circuit whereby it is made effective in duplicate in each of the other circuits.

2. In combination, a transducer giving different delays for different frequencies over a certain frequency range and a delay compensator giving compensatory delays for the respective frequencies; said delay compensator being connected in tandem with the said transducer and comprising a plurality of sections .with certain consecutive sections consolidated by the incorporation of transformers between them. i

3. In combination, a transducer giving diferent delays for different frequencies over a certain frequency range and a delay compensator giving compensator delays for the respective frequencies, said delay compensator being connected in tandem with the said .transdu cerand comprising a plurality of sections with one or more three-winding transformers incorporated between them.

4. In combination, a transducer giving different delays for different frequencies, a

three-winding transformer connected with ferent delays for different frequencies over a certain frequency range anda delay compensator connected with said t ansducer and consisting of a single sectio network comprising a plural ty of 'reactance elements,

these elements having adjusted values to I make the network equivalent to a series of lattice type sections of network.

7. In combination, a transducer giving different delays for different frequencies over a certain frequency range and a delay compensator connected with said transducer and consisting of a single network section having complex impedance elements with their components of respective values to make the section as a whole equivalent to a tandem series of- 'lattice t e network sections each with comparative y simple impedance elements.

8. The method of effecting delay compensation of electric wave currents which are de-' la ed differently for difierent frequencies w ich consists in transmitting the said currents and subjecting them to forces to effect approximately half the desired change and reflecting them back to efl'ect the remaining desired change.

' 9. In combination, a hybrid coil with inut and output terminals and with an absorbmg network and a reflecting network balanced against each other, the reflecting network bein designed to give certain desired difierent elays at respective frequencies.

10. The method of producing a desired degree of phase compensation in electric wave currents which consists in sending them re-' peatedly over the same course subject to compensating forces and thereby cumulating the change'due to going once over the said course.

'11. In combination, a pair of input terminals, a pair of output terminals, a phase compensating network between said pairs of terminals, a transducer having a non-uni-' form delay characteristic connected with one said pair, and means to direct input currents through the network and reflect them back through it to the output terminals. with compensation of delay so as to give an overall uniform delay characteristic.

12. In combination, a transducer giving different delays for difierent frequencies over a certain frequency range and a delay com- 1 pensator in combination therewith, said delay compensator comprising at least one section and composed of a certain number of reactance elements, the said reactance elements being adjusted in value to make the delayfrequencyv characteristic of the said compensatorthe same as of a series of lattice type network sections composed of a greater number of reactance elements and designed to compensate the delay in the said transducer.

In testimony whereof, I have signed my name to this specification this 23rd day of February, 1926.

, HAltRY NYQUIST. 

